Related papers: Some thoughts on multiparameter stochastic process…
Applying non-ergodic quadratic stochastic operator the continual family of weak ergodic non-homogeneous Markov chains is constructed.
We present a multivariate central limit theorem for a general class of interacting Markov chain Monte Carlo algorithms used to solve nonlinear measure-valued equations. These algorithms generate stochastic processes which belong to the…
Many systems are partially stochastic in nature. We have derived data driven approaches for extracting stochastic state machines (Markov models) directly from observed data. This chapter provides an overview of our approach with numerous…
A generalization of differential operators are pseudodifferential operators which are used for reasoning about partial differential equations with variable coefficients. A lot of useful properties about classical pseudodifferential…
We consider a discrete time semi-Markov process where the characteristics defining the process depend on a small perturbation parameter. It is assumed that the state space consists of one finite communicating class of states and, in…
The rigorous linking of exact stochastic models to mean-field approximations is studied. Starting from the differential equation point of view the stochastic model is identified by its Kolmogorov equations, which is a system of linear ODEs…
Multistate Markov models are a canonical parametric approach for data modeling of observed or latent stochastic processes supported on a finite state space. Continuous-time Markov processes describe data that are observed irregularly over…
Markov chain Monte Carlo (MCMC) methods asymptotically sample from complex probability distributions. The pseudo-marginal MCMC framework only requires an unbiased estimator of the unnormalized probability distribution function to construct…
We study the task of learning from non-i.i.d. data. In particular, we aim at learning predictors that minimize the conditional risk for a stochastic process, i.e. the expected loss of the predictor on the next point conditioned on the set…
We introduce a new embarrassingly parallel parameter learning algorithm for Markov random fields with untied parameters which is efficient for a large class of practical models. Our algorithm parallelizes naturally over cliques and, for…
In various practical situations, we encounter data from stochastic processes which can be efficiently modelled by an appropriate parametric model for subsequent statistical analyses. Unfortunately, the most common estimation and inference…
Coarse-graining is a standard method of extracting a simple Markov process from a more complicated one by identifying states. Here we extend coarse-graining to open Markov processes. An "open" Markov process is one where probability can…
Gaussian processes models are widely adopted for nonparameteric/semi-parametric modeling. Identifiability issues occur when the mean model contains polynomials with unknown coefficients. Though resulting prediction is unaffected, this leads…
We propose deterministic timed automata (DTA) as a model-independent language for specifying performance and dependability measures over continuous-time stochastic processes. Technically, these measures are defined as limit frequencies of…
We study general stochastic birth and death processes including delay. We develop several approaches for the analytical treatment of these non-Markovian systems, valid, not only for constant delays, but also for stochastic delays with…
We introduce a generalization of the Adaptive Multilevel Splitting algorithm in the discrete time dynamic setting, namely when it is applied to sample rare events associated with paths of Markov chains. By interpreting the algorithm as a…
We obtain an asymptotic H\"older estimate for expectations of a quite general class of discrete stochastic processes. Such expectations can also be described as solutions to a dynamic programming principle or as solutions to discretized…
We start from the observation that, anytime two Markov generators share an eigenvalue, the function constructed from the product of the two eigenfunctions associated to this common eigenvalue is a duality function. We push further this…
We study large deviation properties of random matricial spectral measures.
In this monograph we develop magnetic pseudodifferential theory for operator-valued and equivariant operator-valued functions and distributions from first principles. These have found plentiful applications in mathematical physics,…